This article aims to review a selection of central topics and examples in logarithmic
conformal field theory. It begins with the remarkable observation of Cardy that the horizontal …

A bstract We find and propose an explanation for a large variety of modularity-related
symmetries in problems of 3-manifold topology and physics of 3d\(\mathcal {N}\)= 2 theories …

We construct a family of 3d quantum field theories $\mathcal T_ {n, k}^ A $ that conjecturally
provide a physical realization--and derived generalization--of non-semisimple mathematical …

Logarithmic conformal field theories (LCFT) play a key role, for instance, in the description of
critical geometrical problems (percolation, self-avoiding walks, etc), or of critical points in …

Abstract The SL (2, ℤ)-representation π on the center of the restricted quantum group at the
primitive 2 p th root of unity is shown to be equivalent to the SL (2, ℤ)-representation on the …

Let $ V $ be a vertex operator algebra with a category $\mathcal {C} $ of (generalized)
modules that has vertex tensor category structure, and thus braided tensor category …

We study the triplet vertex operator algebra W (p) of central charge 1− 6 (p− 1) 2p, p⩾ 2. We
show that W (p) is C2-cofinite but irrational since it admits indecomposable and logarithmic …

We study logarithmic conformal field models that extend the (p, q) Virasoro minimal models.
For coprime positive integers p and q, the model is defined as the kernel of the two minimal …

This is the first part in a series of papers in which we introduce and develop a natural,
general tensor category theory for suitable module categories for a vertex (operator) …

A bstract Logarithmic conformal field theories have a vast range of applications, from critical
percolation to systems with quenched disorder. In this paper we thoroughly examine the …